EP3671266A1 - Verfahren zur entfernungsmessung mit angepasster fourier-transformation, und radarsystem zur umsetzung dieses verfahrens - Google Patents

Verfahren zur entfernungsmessung mit angepasster fourier-transformation, und radarsystem zur umsetzung dieses verfahrens Download PDF

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EP3671266A1
EP3671266A1 EP19210521.1A EP19210521A EP3671266A1 EP 3671266 A1 EP3671266 A1 EP 3671266A1 EP 19210521 A EP19210521 A EP 19210521A EP 3671266 A1 EP3671266 A1 EP 3671266A1
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Prior art keywords
frequency
signal
value
signals
measurements
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EP19210521.1A
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English (en)
French (fr)
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EP3671266B1 (de
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Thierry Mazeau
Patrick Garrec
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Thales SA
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Thales SA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/87—Combinations of radar systems, e.g. primary radar and secondary radar
    • G01S13/874—Combination of several systems for attitude determination
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G01S13/32—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated
    • G01S13/34—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal
    • G01S13/345—Systems for measuring distance only using transmission of continuous waves, whether amplitude-, frequency-, or phase-modulated, or unmodulated using transmission of continuous, frequency-modulated waves while heterodyning the received signal, or a signal derived therefrom, with a locally-generated signal related to the contemporaneously transmitted signal using triangular modulation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/06—Systems determining position data of a target
    • G01S13/08—Systems for measuring distance only
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/50—Systems of measurement based on relative movement of target
    • G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
    • G01S13/60—Velocity or trajectory determination systems; Sense-of-movement determination systems wherein the transmitter and receiver are mounted on the moving object, e.g. for determining ground speed, drift angle, ground track
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G06F17/141—Discrete Fourier transforms
    • G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/38—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation
    • G06F7/48—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices
    • G06F7/544—Methods or arrangements for performing computations using exclusively denominational number representation, e.g. using binary, ternary, decimal representation using non-contact-making devices, e.g. tube, solid state device; using unspecified devices for evaluating functions by calculation
    • G06F7/556—Logarithmic or exponential functions
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/35—Details of non-pulse systems
    • G01S7/352—Receivers
    • G01S7/356—Receivers involving particularities of FFT processing

Definitions

  • the invention relates to the general field of airborne systems, helicopters or aircraft with (airplanes) or without (drones) pilot for example. It relates more particularly to distance measurements carried out by a radar on board one or the other of these vehicles.
  • This operating mode implements the transmission of radio signals by the radar towards the ground and the analysis of signals received by the radar, obtained after the reflection of the radio signals emitted by the ground. Analysis of the time-frequency representations of the signals transmitted and received makes it possible to determine the delay between the signals transmitted and the signals received and to determine the distance which separates the airborne system from the ground.
  • two radio signals denoted e 0 (t) and e 1 (t) are transmitted in the direction of the ground during a time interval T E.
  • the frequency of the first signal e 0 (t) exhibits a positive linear variation during the first half of the time interval [0, T E / 2] and the frequency of the second signal e 1 (t) exhibits a negative linear variation during the second half of the transmission time interval [T E / 2, T E ].
  • the frequencies of the transmitted signals vary in a frequency band B.
  • the signal e 1 (t) corresponds to an equal time translation T E of the signal e 0 (t).
  • the signals e 0 (t) and e 1 (t) emitted are reflected by the ground.
  • the reflected signals are also signals modulated linearly in frequency, their frequencies vary on band B and represent with respect to the transmitted signals, a time shift, a delay, noted ⁇ , and a frequency shift noted f D due to the effect.
  • the reflected signals are then received by the radar system.
  • the figure 1 represents the signals transmitted and the signals received as a function of time.
  • the received signals are then demodulated and converted into digital signals.
  • the determination of the measurement of the distance d separating the radar system from the ground is based on this operating mode on a spectral analysis of the signals received.
  • a time / frequency representation of the transmitted and received signals is made.
  • the signal E 1 (t) represents the value of the frequency of the second signal e 1 (t) at the instant t considered. It appears as a frequency ramp with a coefficient (slope) equal to -K.
  • R 0 (t) represents the value of the frequency of the signal r 0 (t) at the instant t considered. It appears as a frequency ramp similar to the signal E 0 (t) but offset by a time interval ⁇ , on the abscissa axis and by a frequency f D on the frequency axis (the axis of the ordered).
  • R 1 (t) represents the value of the frequency of the signal r 1 (t) at the instant t considered. It appears as a frequency ramp similar to the signal E 1 (t) but offset by a time interval ⁇ on the abscissa axis and by a frequency f D on the frequency axis (the ordinate axis ).
  • the offset between the first signal sent e 0 (t) and the received signal r 0 (t) can also be represented in the frequency domain by making the difference between the value of the frequency R 0 (t) representing the value of the frequency of the received signal r 0 (t) and the value of the frequency E 0 (t) representing the value of the frequency of the first signal transmitted e 0 (t) at the instant considered.
  • the offset between the second signal sent e 1 (t) and the received signal r 1 (t) can be represented in the frequency domain by making the difference between the value of the frequency R 1 (t) representing the value of the frequency of the received signal r 1 (t) and the value of the frequency E 1 (t) representing the value of the frequency of the second signal transmitted e 1 (t) at the instant considered.
  • the determination of the frequency magnitude D thus makes it possible to determine the delay ⁇ .
  • the frequency difference D is a quantity with value always strictly positive since it is proportional to the time delay and therefore to the distance.
  • the measurement of the distance d separating the radar system from the ground is determined by performing a spectral analysis of the signal D.
  • the spectrum thus formed is made up of frequency samples.
  • the determination of the spectrum of the signal D by the determination of the frequency samples allows, according to the equation (Math. 10), to determine frequency measurements (given by 2 K ⁇ ) of the signal D at each instant considered and thereafter to determine the delay ⁇ and the distance d that one wishes to measure.
  • the figure 2 represents the spectrum of the signal x (t) sampled on M points at the frequency F ech .
  • the spectrum of the signal x (t) is presented as an elementary spectrum of equal width F ec , replicated in the frequency space with a periodicity equal to F ec .
  • the frequency steps of the FFT are spaced constantly.
  • the spectral decomposition of the signal x (t) makes it possible to unambiguously determine the frequency spectrum (the center frequency) of the signal X (F) provided that the frequency band occupied by X (F) is less than F ec / 2.
  • the frequency band occupied by X (F) is greater than this value, there is an ambiguity in frequency due to the aliasing of the spectrum of X (F) in a band [- F ech / 2, F ech / 2] replicated periodically around frequencies multiple of the frequency F ech .
  • the frequency of the signal X (F) (and therefore the delay ⁇ ) can only be determined modulo the sampling frequency F ech .
  • ambiguities is induced by the compromise to be achieved between the use of a sampling frequency sufficient to avoid any spectral ambiguity, the number of measurements on which the FFT must be carried out. to obtain the desired spectral resolution and the computing capacity available to perform an FFT on the desired number of points.
  • the transmitted signals can consist of a first transmitted radio signal and a second transmitted radio signal
  • the received signals consisting of a first received signal and a second received signal
  • the first signal received corresponding to the signal obtained by the reflection of the first signal emitted by the ground
  • the second received signal corresponding to the signal obtained by the reflection of the second signal emitted by the ground
  • the calculation means being configured to determine the frequency quantity by calculating the difference between a first frequency signal and a second frequency signal, the first frequency signal corresponding to the difference between the representation the frequency of the first received signal and the frequency representation of the first transmitted signal, the second frequency signal corresponding to the difference between the frequency representation of the second received signal and the frequency representation of the second transmitted signal.
  • the calculation means can be configured to sample the frequency quantity according to a sampling period, the calculation means being configured to determine a minimum sampling period as a function of a maximum frequency value and for determining a number of samples of the sampled signal based on a minimum frequency value and the minimum sampling period.
  • the calculation means can be configured to determine an intermediate parameter as a function of the distance measurement precision value, the intermediate parameter being calculated by dividing a first value by a second value, the first value being calculated by adding the measurement precision value to the value two, the second value being calculated by subtracting the distance measurement precision value from the value two, the calculation means being configured to determine the number of frequency measurements as a function of '' a minimum frequency value, a maximum frequency value and the intermediate parameter.
  • the calculation means can be configured to determine the number of frequency measurements by dividing a first logarithmic function by a second logarithmic function, the first logarithmic function corresponding to the natural logarithm of the ratio between the maximum value frequency and the minimum frequency value, the second logarithmic function corresponding to the natural logarithm of the intermediate parameter.
  • the embodiments of the invention make it possible to improve and adapt the distance resolution as a function of the radar-ground distance measured without increasing the number of FFT measurements used to perform the spectral decomposition of the frequency signal derived from the sampling of the frequency signal dependent on the frequency representations of the transmitted and received signals.
  • the embodiments of the invention allow distance measurements by adapted Fourier transform by preserving the accuracy of the distance measurement (which is constant) as a function of the distance measured (or the frequency resolution) and by adapting the no frequency of FFT measurements or calculations by decimation at the measured distance.
  • the embodiments of the invention make it possible to adjust the frequency resolution as a function of the distance measured.
  • the embodiments of the invention allow distance measurements which do not maintain a constant frequency resolution as a function of the frequency increase to hold a value of constant distance measurement accuracy. This is achieved by spacing the sampling periods by decimation as a function of the frequency to be measured.
  • the embodiments of the invention provide a radar system and a method for determining radar-to-ground distance measurements according to an operating mode which implements the spectral analysis of the frequency representations of the radio signals emitted in the direction of the ground and of the signals received following the reflection of signals emitted by the ground.
  • the radar system and the method according to the invention can be used for example in airborne systems, helicopters or aircraft with or without pilot for example.
  • a radar system 300 configured to determine distance measurements separating the radar from the ground is illustrated, according to certain embodiments of the invention.
  • the radar system 300 is configured to determine the distance measurements using the operating mode based on the emission of radio signals to the ground, the reception of these signals after reflection by the ground, and the spectral analysis of the signals transmitted and received.
  • the radar system 300 can comprise transmission and reception means 301 configured to transmit two radio signals e 0 (t) and e 1 (t) towards the ground during a time interval T E and to receive the signals obtained by the reflection of the two signals emitted by the ground, noted r 0 (t) and r 1 (t).
  • the frequency of the first signal e 0 (t) exhibits a positive linear variation during the first half of the time interval [0, T E / 2] and the frequency of the second signal e 1 (t) exhibits a negative linear variation during the second half of the transmission time interval [T E / 2, T E ].
  • the frequencies of the transmitted signals vary in a frequency band B.
  • the radio signals e 0 (t) and e 1 (t) are radiated by the transmission means 301, are linearly modulated in frequency as a function of time and have as expressions those given to the equation (Math.1).
  • the signals e 0 (t) and e 1 (t) emitted are reflected by the ground.
  • the reflected signals are also signals modulated linearly in frequency, their frequencies vary on band B and represent with respect to the transmitted signals, a time offset ⁇ and a frequency offset noted f D due to the Doppler effect generated by the movement of the carrier.
  • the signals received by the reception means 301 comprise a first received signal r 0 (t) corresponding to the signal received following the reflection of the first signal transmitted e 0 (t) by the ground and a second received signal r 1 (t) corresponding to the signal received following the reflection of the second signal emitted e 1 (t) by the ground.
  • the signals received have as expressions those given in equations (Math.2) and (Math.3).
  • the radar system 300 may include a mixer 303 configured to demodulate (or transpose) the received signals with the replica of the transmitted signals using an analog digital encoder (ADC) 305 configured to convert the transposed signals into digital signals.
  • ADC analog digital encoder
  • the radar system 300 can also include calculating means 307 configured to perform a spectral analysis of the converted demodulated signals in order to determine distance measurements separating the radar from the ground from frequency measurements.
  • the calculation means 307 can be configured to determine the frequency representations of the signals transmitted and the received signals. For the instants t between 0 and T E / 2, the frequency representations E 0 (t) and R 0 (t) of the first signal sent e 0 (t) and of the first signal received r 0 (t) are given respectively by equations (Math.4) and (Math.6). For the instants t between T E / 2 and T E , the frequency representations E 1 (t) and R 1 (t) of the second signal sent e 1 (t) and of the second received signal r 1 (t) are given respectively by the equations (Math.5) and (Math.7)
  • the calculation means 307 can be configured to determine a frequency quantity D as a function of the frequency representations of the signals transmitted and of the signals received. More precisely, the calculation means 307 can be configured to determine the frequency quantity D by calculating the difference between a first frequency signal ⁇ F 0 and a second frequency signal ⁇ F 1 , the first frequency signal ⁇ F 0 corresponding to the difference between the frequency representation of the first received signal R 0 (t) and the frequency representation of the first transmitted signal E 0 (t) as expressed in equation (Math.8), the second frequency signal ⁇ F 1 corresponding to the difference between the frequency representation of the second signal received R 1 (t) and the frequency representation of the second signal emitted E 1 (t), as expressed in the equation (Math.9).
  • the calculation means 307 can be configured to determine the time offset ⁇ and therefore the radar-ground distance measurements from the frequency quantity D according to the relationship given by the equation ( Math. 10). More specifically, the calculation means 307 can be configured to determine measurements in radar-ground distance by performing a spectral analysis of the frequency magnitude D.
  • the calculation means 307 can be configured to sample the frequency quantity represented by the signal x (t) on Z points (or samples).
  • the distance measurements according to the invention are determined by determining a number N of frequency measurements by suitable FFT applied to the sampled signal while maintaining a constant distance measurement precision value P.
  • the calculation means 307 can be configured to determine a number N of frequency measurements as a function of a given distance measurement precision value P. More precisely, the calculation means 307 can be configured to determine an intermediate parameter L as a function of a given distance measurement precision value P , the intermediate parameter being calculated by dividing a first value by a second value, the first value (2+ P ) being calculated by adding said measurement accuracy to the value two, the second value (2- P ) being calculated by subtracting the value for measurement accuracy P of distance from the value two.
  • the calculation means 307 can be configured to determine the number N of frequency measurements to be carried out by the FFT, that is to say the number of spectral samples of the FFT, as a function of a minimum frequency value, a maximum frequency value and the intermediate parameter.
  • the distance measurement precision value can be given as a percentage.
  • the FFT adapted according to the invention makes it possible to adapt the frequency step of the frequency measurements by FFT, by decimation, to the measured distance, while keeping a constant distance measurement precision value as a function of the measured frequency. In fact, in order to maintain a constant distance measurement precision value, it is not necessary, according to the invention, to keep a constant frequency resolution as a function of the frequency increase.
  • the values of f j are distributed in a non-constant manner and the values of x m are samples spaced differently in time as a function of the measured frequencies f j .
  • the decimation of the sampled signal thus depends on the frequency measured as illustrated in the decimation report for the j th frequency measurement f j given by 1 / (L ( (Nj) ).
  • the invention also provides a method for determining radar-ground distance measurements by spectral analysis of radio signals transmitted and received by a radar system while maintaining a constant distance measurement accuracy value as a function of the increase in the measured frequencies. .
  • the method may include steps for transmitting and receiving two radio signals and steps for processing the received signals.
  • two radio signals e 0 (t) and e 1 (t) can be emitted towards the ground during a time interval T E such that The frequency of the first signal e 0 (t) exhibits a positive linear variation during the first half of the time interval [0, T E / 2] and the frequency of the second signal e 1 (t) exhibits a negative linear variation during the second half of the transmission time interval [T E / 2, T E ].
  • the frequencies of the transmitted signals vary in a frequency band B.
  • the radio signals e 0 (t) and e 1 (t) are linearly frequency modulated as a function of time and have as expressions those given in the equation (Math.1 ).
  • the signals obtained by the reflection of the signals emitted by the ground can be received.
  • the received signals include a first received signal r 0 (t) corresponding to the signal received following the reflection of the first signal transmitted e 0 (t) by the ground and a second received signal r 1 (t) corresponding to the signal received following the reflection of the second signal emitted e 1 (t) by the ground.
  • the signals received have as expressions those given in equations (Math.2) and (Math.3).
  • Step 401 may include a sub-step for demodulating the received signals and converting the demodulated signals into analog signals.
  • step 402 frequency representations of the transmitted and received signals can be determined.
  • the frequency representations E 0 (t) and R 0 (t) of the first signal emitted e 0 (t) and of the first signal received r 0 (t) can be determined respectively by the equations (Math.4) and (Math.6).
  • the frequency representations E 1 (t) and R 1 (t) of the second signal sent e 1 (t) and of the second signal received r 1 (t) can be determined by equations (Math.5) and (Math.7) respectively.
  • a frequency quantity D can be determined as a function of the frequency representations of the signals transmitted and of the signals received. More precisely, the frequency quantity D can be determined by calculating the difference between a first frequency signal ⁇ F 0 and a second frequency signal ⁇ F 1 , the first frequency signal ⁇ F 0 corresponding to the difference between the frequency representation of the first received signal R 0 ( t) and the frequency representation of the first transmitted signal E 0 (t) as expressed in equation (Math.8), the second frequency signal ⁇ F 1 corresponding to the difference between the frequency representation of the second received signal R 1 (t) and representation frequency of the second signal emitted E 1 (t), as expressed in the equation (Math. 9).
  • the number N of measurements can be determined in step 404 as a function of a constant distance measurement precision value.
  • step 405 radar-ground distance measurements can be determined from the frequency measurements determined in step 404.
  • the Figure 5 is a flowchart illustrating step 404 of determining frequency measurements according to certain embodiments of the invention.
  • step 500 a minimum value of frequency f 0 , a maximum value of frequency f N , a value of constant measurement precision P, and the frequency band B of the transmitted signals can be received.
  • a number of samples Z of the sampled signal to be acquired can be determined according to the sampling period and the minimum frequency value as expressed in the equation (Math.14).
  • an intermediate parameter L can be determined as a function of the measurement precision value P as expressed in the equation (Math.15).
  • the number N of frequency measurements to be performed by the FFT can be determined as a function of the minimum frequency value f 0 , the maximum frequency value f N and the intermediate parameter L as given in the equation (Math.16).
  • the FFT frequency measurements are given by the equation (Math.17).
  • the invention further provides a computer program product comprising code instructions for performing the steps of the method when said program is executed on a computer.
  • routines executed to implement the embodiments of the invention may be referred to herein as "computer program code” or simply "code program ".
  • the program code typically includes computer readable instructions which reside at various times in various memory and storage devices in a computer and which, when read and executed by one or more processors in a computer, bring the computer to perform the operations necessary to execute the operations and / or the elements specific to the various aspects of the embodiments of the invention.
  • the instructions of a program, readable by computer, to carry out the operations of the embodiments of the invention can be, for example, the language assembly code, or source code or object code written in combination with one or more programming languages.

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  • General Physics & Mathematics (AREA)
  • Remote Sensing (AREA)
  • Radar, Positioning & Navigation (AREA)
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  • Computational Mathematics (AREA)
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EP19210521.1A 2018-12-20 2019-11-21 Verfahren zur entfernungsmessung mit angepasster fourier-transformation, und radarsystem zur umsetzung dieses verfahrens Active EP3671266B1 (de)

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US10976461B2 (en) * 2017-10-17 2021-04-13 California Institute Of Technology Sub-surface imaging of dielectric structures and voids via narrowband electromagnetic resonance scattering
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EP3671266B1 (de) 2022-06-29
FR3090892A1 (fr) 2020-06-26
US20200200893A1 (en) 2020-06-25
US11604270B2 (en) 2023-03-14

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